4. Suppose that a firm in a perfectly competitive industry faces the following short-run cost

function: TC = 0.2q3 – 1oq2 + 30oq.

a. What will be the long-run equilibrium price and per firm quantity? (2 points)

b. The market demand is given by Qo = 1000 – P. How many total firms will there be at the

long-run equilibrium? (1 point)

c. If a negative demand shock causes the market demand to decrease to

QD = 800 – 2P, how will the individual firms and constant cost industry in general respond to

the negative demand shock in the short run and the long run? (3points)

d. How would the industry response be different if it were a decreasing cost industry? (4pts)

5. For the cost function C = q’8 v” w” demonstrate whether the following statements are true

or false:

I. The function exhibits decreasing average cost. (3pts)

II. The function is homogeneous of degree 1 in v and w. (3pts)

III. The elasticity of marginal cost with respect to v exceeds the elasticity with respect to w.

(4ptS)

6. What does the marginal rate of technical substitution (MRTS) of labor for capital measure?

How does it relate to the underlying production function? Illustrate it in the K,L space. (5pts)

7. Can a production function exhibit increasing returns to scale along with diminishing marginal

productivities for all inputs? (5pts)

## Sample Solution