3. The market for lemon has 10 potential consumers, each having an individual demand
curve P = 101 - 10Qi, where P is price in dollars per cup and Qi is the number of cups
demanded per week by the ith consumer. Find the market demand curve using algebra.
Draw an individual demand curve and the market demand curve. What is the quantity
demanded by each consumer and in the market as a whole when lemon is priced at P =
$1/cup?
4. The demand for tickets to an Ethiopian Camparada film is given by D(p)= 200,000-
10,000p, where p is the price of tickets. If the price of tickets is 12 birr, calculate price
elasticity of demand for tickets and draw the demand curve
5. Given market demand Qd = 50 - P, and market supply P = Qs + 5
A) Find the market equilibrium price and quantity?
B) What would be the state of the market if market price was fixed at Birr 25 per unit?
C) Calculate and interpret price elasticity of demand at the equilibrium point.
6. When price of tea in local café rises from Br. 10 to 15 per cup, demand for coffee rises
from 3000 cups to 5000 cups a day despite no change in coffee prices.
A) Determine cross price elasticity.
B) Based on the result, what kind of relation exists between the two goods?
7. What is the basic difference between cardinal and ordinal approaches of utility?
8. A rational consumer spends all of her income on two goods: Apple and Banana.
Suppose the last dollar spent on Apple increased her total utility from 60 utils to 68 utils
and the last dollar spent on Banana increased her total utility from 25 utils to 29 utils. If
the price of a unit of Apple is 2 Birr, what is the price of a unit of Banana at equilibrium?
9. Suppose the production function is given by Q(L,K) = L3/4K
1/4 Assuming capital is
fixed, find APL and MPL.
10. Given a short run cost function as TC = 1/3Q3
-2Q2
+60Q+100 , find the minimum
value of AVC and MC.
11. What are the similarities and differences between oligopoly and monopolistically
competitive market structure?
12. A firm operates in a perfectly competitive market. The market price of its product is
4 birr and the total cost function is given by TC= 1/3Q3
-5Q2
+20Q+50, wh�
3. To find the market demand curve, we need to sum up the individual demand curves of each consumer.
The individual demand curve for each consumer is P = 101 - 10Qi, where Qi is the number of cups demanded per week by the ith consumer.
The total quantity demanded by all consumers can be found by summing up the quantities demanded by each consumer at a given price:
Qd = Q1 + Q2 + Q3 + ... + Q10
Since each consumer has the same demand curve, we can substitute Qi with Q/n, where n is the number of consumers.
Qd = Q1/n + Q2/n + Q3/n + ... + Qn/n
Qd = (Q1 + Q2 + Q3 + ... + Qn)/n
The market demand curve can now be expressed as:
P = 101 - 10(Q1 + Q2 + Q3 + ... + Qn)/n
P = 101 - 10Qd/n
To find the quantity demanded by each consumer and in the market as a whole when lemon is priced at P = $1/cup, we simply substitute P with 1 and solve for Qd:
1 = 101 - 10Qd/n
10Qd/n = 100
Qd = 10n
Since there are 10 potential consumers in the market, the quantity demanded by each consumer and in the market as a whole when lemon is priced at P = $1/cup is 10 cups for each consumer and a total of 100 cups for the market.
4. The price elasticity of demand can be calculated using the formula:
E = (% change in quantity demanded) / (% change in price)
Given that the price of tickets is 12 birr, we can calculate the quantity demanded at this price using the demand function:
D(12) = 200,000 - 10,000(12)
D(12) = 200,000 - 120,000
D(12) = 80,000
Now let's calculate the price elasticity of demand:
E = ((80,000 - 200,000) / (200,000)) / ((12 - 10) / (10))
E = (-0.6) / (0.2)
E = -3
The price elasticity of demand for tickets is -3. This means that a 1% increase in price will result in a 3% decrease in quantity demanded.
To draw the demand curve, we can plot the quantity demanded on the y-axis and the price on the x-axis. Assuming the quantity demanded is in thousands and the price is in birr, the demand curve can be plotted as:
Quantity Demanded (thousands) = 200 - 10p
5. A) To find the market equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied:
Qd = Qs
50 - P = P - 5
50 + 5 = 2P
55 = 2P
P = 27.5
Substituting the equilibrium price back into the demand or supply equation, we can find the equilibrium quantity:
Qd = 50 - 27.5
Qd = 22.5
Qs = 27.5 + 5
Qs = 32.5
The market equilibrium price is Birr 27.5 per unit and the equilibrium quantity is 22.5 units.
B) If the market price was fixed at Birr 25 per unit, the quantity demanded would be:
Qd = 50 - 25
Qd = 25
The quantity supplied would be:
Qs = 25 + 5
Qs = 30
Since the quantity demanded is less than the quantity supplied, there would be excess supply in the market.
C) To calculate the price elasticity of demand at the equilibrium point, we can use the formula:
E = (% change in quantity demanded) / (% change in price)
Since the demand equation is Qd = 50 - P, the price elasticity of demand can be calculated as:
E = ((Qd - Qd') / (Qd')) / ((P - P') / (P))
E = ((22.5 - 22.5) / (22.5)) / ((27.5 - 27.5) / (27.5))
E = 0 / 0
The price elasticity of demand at the equilibrium point is undefined. This means that a change in price will not result in a change in quantity demanded at the equilibrium point.
6. A) To determine the cross price elasticity, we need to find the percentage change in demand for coffee in response to a change in the price of tea.
The percentage change in demand for coffee can be calculated as:
(% change in demand for coffee) = ((new demand - old demand) / old demand) * 100%
(% change in demand for coffee) = ((5000 - 3000) / 3000) * 100%
(% change in demand for coffee) = 2000 / 3000 * 100%
(% change in demand for coffee) = 66.67%
The percentage change in price of tea is:
(% change in price of tea) = ((new price - old price) / old price) * 100%
(% change in price of tea) = ((15 - 10) / 10) * 100%
(% change in price of tea) = 5 / 10 * 100%
(% change in price of tea) = 50%
The cross price elasticity is:
E = (% change in demand for coffee) / (% change in price of tea)
E = 66.67% / 50%
E = 1.33
B) Based on the result, a positive cross price elasticity of 1.33 means that tea and coffee are substitutes. This means that an increase in the price of tea leads to an increase in the demand for coffee.
7. The basic difference between the cardinal and ordinal approaches of utility is in how they measure and compare utility.
In the cardinal approach, utility is assumed to be measurable and quantifiable. Consumers assign specific cardinal values or numbers to the satisfaction or utility they derive from consuming goods or services. This allows for direct comparison of utility between different goods or consumption choices.
In the ordinal approach, utility is not measurable or quantifiable, but rather it provides an ordering or ranking of preferences. Consumers can rank their preferences for different goods, but the actual numerical value of the utility is not important. The focus is on the relative ranking of preferences, not on the specific magnitude of utility.
8. To find the price of a unit of Banana at equilibrium, we can use the concept of marginal utility and the given information about total utility.
The marginal utility of the last dollar spent on Apple can be calculated as the difference in total utility before and after spending that dollar:
MU = 68 - 60
MU = 8
The marginal utility of the last dollar spent on Banana can be calculated as the difference in total utility before and after spending that dollar:
MU = 29 - 25
MU = 4
Since the price of a unit of Apple is 2 Birr, the marginal utility per Birr spent on Apple is:
MU/Price = 8/2
MU/Price = 4
The marginal utility per Birr spent on Banana is:
MU/Price = 4/Pb
Since the marginal utility per Birr spent on each good should be equal at equilibrium, we can equate the two expressions:
4 = 4/Pb
Pb = 1
Therefore, the price of a unit of Banana at equilibrium is 1 Birr.
9. Assuming capital is fixed, the average product of labor (APL) can be calculated as:
APL = Q / L
And the marginal product of labor (MPL) can be calculated as the derivative of the production function with respect to labor:
MPL = (∂Q/∂L)
Given that the production function is Q(L,K) = L^(3/4) * K^(1/4), where K is fixed, we can substitute K with a constant value and calculate APL and MPL.
APL = Q / L
APL = (L^(3/4) * K^(1/4)) / L
APL = L^(-1/4) * K^(1/4)
MPL = (∂Q/∂L) = (∂/∂L) (L^(3/4) * K^(1/4))
MPL = (3/4) * L^(-1/4) * K^(1/4)
MPL = (3/4) * APL
Therefore, the average product of labor is APL = L^(-1/4) * K^(1/4) and the marginal product of labor is MPL = (3/4) * APL.
10. To find the minimum value of AVC and MC, we need to take the derivative of the cost function with respect to quantity and set it equal to zero.
The total cost function is given by TC = 1/3Q^3 - 2Q^2 + 60Q + 100.
The average variable cost (AVC) can be calculated as:
AVC = VC / Q
The variable cost (VC) can be found by subtracting the fixed cost (FC) from the total cost (TC):
VC = TC - FC
The marginal cost (MC) can be calculated as the derivative of the total cost function with respect to quantity:
MC = dTC / dQ
Taking the first derivative of the total cost function:
dTC / dQ = Q^2 - 4Q + 60
Setting the first derivative equal to zero:
Q^2 - 4Q + 60 = 0
Solving this quadratic equation, we find two values for Q: Q = 6 and Q = 10.
Substituting these values back into the total cost function, we can find the corresponding values for TC:
TC(6) = 1/3(6^3) - 2(6^2) + 60(6) + 100
TC(6) = 72
TC(10) = 1/3(10^3) - 2(10^2) + 60(10) + 100
TC(10) = 380
The minimum value of AVC is found at Q = 6, where AVC = VC / Q:
AVC = (TC - FC) / Q
AVC(6) = (72 - 100) / 6
AVC(6) = -28 / 6
AVC(6) = -4.67
The minimum value of MC is also found at Q = 6, where MC = dTC / dQ:
MC = dTC / dQ
MC(6) = 6^2 - 4(6) + 60
MC(6) = 36 - 24 + 60
MC(6) = 72
Therefore, the minimum value of AVC is -4.67 and the minimum value of MC is 72.
11. The similarities between oligopoly and monopolistically competitive market structures include the existence of multiple firms and a degree of market power.
In both oligopoly and monopolistic competition, there are multiple firms competing in the market. This means that buyers have a choice of different products or brands.
Both market structures also involve a degree of market power. In oligopoly, a small number of firms dominate the market, which gives them the ability to influence prices and output decisions. In monopolistic competition, each firm has some degree of control over price and quantity due to product differentiation.
However, there are also important differences between oligopoly and monopolistic competition.
In oligopoly, there are a small number of large firms that dominate the market. These firms may collude to increase their market power or engage in non-price competition, such as advertising or innovation. Prices in an oligopoly tend to be relatively stable due to the interdependence of firms.
In monopolistic competition, there are many small firms that compete by offering differentiated products. Each firm has some degree of control over the price of its own product. Prices in a monopolistically competitive market can vary due to product differentiation and advertising.
12. In a perfectly competitive market, the market price is determined by the intersection of the market demand and supply curves. The total cost (TC) function represents the cost of production for the firm, and the difference between the market price and the firm's average total cost (ATC) determines whether the firm earns a profit or incurs a loss.
The market price of the product being produced by the firm is given as 4 birr, and the total cost function is TC = 1/3Q^3 - 5Q^2 + 20Q + 50.
To find the equilibrium quantity, we set the market price equal to the firm's ATC:
4 = (1/3Q^3 - 5Q^2 + 20Q + 50) / Q
4Q = 1/3Q^3 - 5Q^2 + 20Q + 50
Simplifying the equation:
1/3Q^3 - 5Q^2 + 16Q + 50 = 0
To find the equilibrium quantity, we can solve this cubic equation. However, without further information about the shape of the cost function, it is not possible to determine the exact equilibrium quantity.
To determine whether the firm earns a profit or incurs a loss at the equilibrium quantity, we compare the market price with the firm's ATC. If the market price is above the ATC, the firm earns a profit. If the market price is below the ATC, the firm incurs a loss.
Unfortunately, without specific information about the shape of the cost function and the equilibrium quantity, it is not possible to determine the profitability of the firm in this case.