1. Suppose that the market of laptops is given by following supply and demand curves given below:
Qd = 5000 − 3p
Qs = 1000 + p.
Answer the following questions on excel sheet using the above demand and supply equations.
i) Take the range of values for the price from $1 to $30 and calculate corresponding demand and supply quantities.
ii) Using the values computed above plot the graph of demand and supply curves on the same graph.
iii) Using the graph above find the market clearing price and quantity for the market of laptops.
iv) Compute the point demand and supply elasticity for all the values of demand and supply curve.
v) If the price of a laptop is set at $2000 then find the amount of laptops that producers will be willing to supply and amount of laptops consumers will be willing to buy at this price level. Will there be any surplus or shortage created at this price.
ans
i) To calculate the corresponding demand and supply quantities for the given price range, we need to substitute each price value from $1 to $30 into the demand and supply equations.
In Excel, create a column for price with values ranging from $1 to $30. Then, in the adjacent columns, use the demand and supply equations to calculate the corresponding quantities.
For the demand equation:
Column A: Price (Values from $1 to $30)
Column B: Quantity Demanded (Formula: =5000-3*A1)
For the supply equation:
Column C: Quantity Supplied (Formula: =1000+A1)
ii) To plot the graph of the demand and supply curves, select the price and quantity columns you created in Excel. Then, insert a line graph using the selected data. You should have two lines, one representing the demand curve and the other representing the supply curve.
iii) On the graph, the market clearing price and quantity occur where the demand and supply curves intersect. Identify the point where the lines intersect and note the corresponding price and quantity values. This will be the market clearing price and quantity for the market of laptops.
iv) To compute the point demand and supply elasticity for all the values of the demand and supply curves, you can use the following formulas:
Demand elasticity:
E_d = (% change in quantity demanded) / (% change in price)
E_d = (dQd/dP) * (P/Qd)
Supply elasticity:
E_s = (% change in quantity supplied) / (% change in price)
E_s = (dQs/dP) * (P/Qs)
In Excel, you can calculate the elasticity for each price point by first finding the numerical derivative of the corresponding quantity equation (Qd or Qs) with respect to price (P), and then multiplying it by the ratio of price (P) to quantity (Qd or Qs). Apply this formula for each price value in the range.
v) If the price of a laptop is set at $2000, you can find the corresponding quantities of laptops that producers are willing to supply and consumers are willing to buy by substituting the price value into the supply and demand equations.
For the demand equation:
Qd = 5000 - 3*2000
For the supply equation:
Qs = 1000 + 2000
Calculate the results to find the amount producers are willing to supply and consumers are willing to buy. If the quantity supplied is greater than the quantity demanded, there will be a surplus. If the quantity demanded is greater than the quantity supplied, there will be a shortage.