problem set 3 6
1.Let a firm’s marginal cost curve be MC = 5 + Q/100.
a. Find the profit maximizing quantity if this firm is a price taker and faces a price of P = $12.
b. Find the profit maximizing quantity if this firm faces a marginal revenue curve of
MR = 15 – Q/100
2.Let the market demand curve for a good be: P = 50 – Q/10.
a. Recall that if the market demand curve is linear, the marginal revenue curve is also linear, with the same price-axis intercept and a slope equal to twice the slope of the demand curve.Write out the marginal revenue curve for this market demand curve.
b. The elasticity of demand can be written as (1/slope)*(P/Q).Find the elasticity of demand for this market demand curve at the following quantities: Q = 50, 150, 250, 350, 450.
c. Verify that the demand curve is elastic at quantities where marginal revenue is positive and inelastic at quantities where marginal revenue is negative.
3.Let a perfectly competitive industry have 100 identical firms with a marginal cost curve given by MC = Q/2.
a. Construct the short run industry supply curve with 100 firms.
b. Let the market demand curve be Q = 4000 – 200*P.Find the short run equilibrium price, industry quantity, and firm quantity.
c. This is a constant cost industry with a cost of $8.Will firms be making profits or losses in the short run equilibrium in b?
d. Find the long run equilibrium price, industry quantity, firm quantity, number of firms, and profit for each firm.
4.Draw a pair of graphs to show the short run and long run equilibrium effects of each of the different events or shocks in a perfectly competitive industry.Assume the industry is in long run equilibrium before the event occurs.Use only one set of cost curves for the firm, like in my lecture notes.(Separate SR and LR cost curves just make the diagram too messy.)Draw the answer for each part of this question on separate diagrams.
a. An increase in demand in an increasing cost industry.
b. A decrease in demand in an increasing cost industry.
c. An increase in the average and marginal cost curves in a constant cost industry.
5.Draw a properly sized Edgeworth Box for each of the following initial endowments.
|
Person A |
Person B |
|||
|
Food |
Clothes |
Food |
Clothes |
|
|
a |
10 |
0 |
0 |
10 |
|
b |
7 |
5 |
3 |
10 |
|
c |
5 |
15 |
10 |
5 |
|
d |
3 |
12 |
17 |
8 |
6.Draw an Edgeworth Box diagram with an initial endowment.Show the gains from trade relative to this endowment point assuming that each person has normal shaped indifference curves.Show the Pareto Efficient points that are within the region of gains from trade relative to the initial endowment.Make sure that your initial endowment point is not Pareto Efficient.
