q = 5,000 - 100p

tc= 10,000 - 10q
plot the demand curve
marginal revenue curve
marginal cost curve
profit maximising price, quantity, and profits

MC=MR UNDER COMPETITIVE MARKET

FIRST DIFFERENTIATED MC = 10
MR=5000-0.02Q
MC=MR THEN EQUAL FIND Q
10=5000-0.02Q
Q=2000UNITS
P=5000-0.01Q WHEN Q=2000 SUBSTITUTE
P=K30
PROFIT=TR-TC
P=K30000

To plot the demand curve, we need to find the relationship between quantity (q) and price (p). The demand equation given is q = 5,000 - 100p. This equation represents a linear demand curve as it is a linear relationship between quantity and price. To plot the demand curve, we can create a table by selecting some values for price and calculating the corresponding quantity. Let's say we choose three price points:

1. When p = 0, q = 5,000 - 100(0) = 5,000.
2. When p = 50, q = 5,000 - 100(50) = 5,000 - 5,000 = 0.
3. When p = 100, q = 5,000 - 100(100) = 5,000 - 10,000 = -5,000.

The negative quantity (-5,000) does not make sense in this context, so we will disregard it. Now we have two points (0, 5,000) and (50, 0). Plot these points on a graph with the quantity (q) on the y-axis and price (p) on the x-axis. Connect the points with a straight line, and you have your demand curve.

To calculate the marginal revenue curve, we need to find the marginal revenue corresponding to each quantity level. Marginal revenue is the change in total revenue resulting from a one-unit change in quantity. We can calculate marginal revenue using the formula:

MR = ΔTR / Δq

where MR is marginal revenue, ΔTR is the change in total revenue, and Δq is the change in quantity. In this case, total revenue is given by TR = p * q, where p is the price and q is the quantity. From the demand equation q = 5,000 - 100p, we can derive the revenue equation TR = p * (5,000 - 100p).

To calculate the change in revenue, we can subtract the revenue at one quantity level from the revenue at the next quantity level. Let's calculate the marginal revenue for two quantity levels, say q1 and q2:

ΔTR = (p * (5,000 - 100p)) at q2 - (p * (5,000 - 100p)) at q1
Δq = q2 - q1

Replace q2 and q1 with the specific values you choose and calculate the marginal revenue for the chosen quantity levels. Repeat this process for different quantity levels to get a range of marginal revenue values.

To plot the marginal cost curve, we need the total cost function. Total cost (TC) is given by TC = 10,000 - 10q. Similar to calculating marginal revenue, marginal cost (MC) is the change in total cost resulting from a one-unit change in quantity. To calculate marginal cost, use the formula:

MC = ΔTC / Δq

where MC is the marginal cost, ΔTC is the change in total cost, and Δq is the change in quantity.

Similarly, calculate the marginal cost for different quantity levels by subtracting the total cost at one quantity level from the total cost at the next quantity level, then divide by the change in quantity.

To find the profit-maximizing price and quantity, we need to equate marginal revenue (MR) and marginal cost (MC) because profit is maximized when MR = MC. Set up an equation for MR and MC by substituting the respective formulas:

MR = ΔTR / Δq
MC = ΔTC / Δq

Then solve the equation to find the price and quantity at which MR equals MC. Plug these values into the demand equation q = 5,000 - 100p or the total cost equation TC = 10,000 - 10q to calculate the corresponding profits.