1. Gump's Shrimp has the production function,

q = K3/4L1/4.

Where q is the number of shrimps per hour, L is the number of workers and K is the number of boats. Suppose that PL = $30/hour and PK = $20/hour.

a. Draw and label an isocost function for C = $300/hour. (2 pts)

b. What is Gump's marginal product of labor (MPL)? (1 pt)

c. What is Gump's marginal product of capital (MPK)? (1 pt)

d. Suppose Gump is stuck with 4 boats in the short run. Find Gump's short-run total cost function. (2 pts)

e. What is Gump's short-run average total cost function, average variable cost function, and marginal cost function? (3 pts)

f. Now Gump is in the long-run. Derive Gump's long-run total cost function (LRTC). (3 pts)

2. Consider the Saxbys coffee shop in Bethlehem. Suppose the wage is w = $2, and the cost of capital is r = $1, and their production function for cups of coffee is

q = 2K0.5L0.5.

a. What is the least cost input combination required to produce 40 cups of coffee? (5 pts)

b. Suppose instead that capital was fixed at 4 units. What would be the implications for labor usage and total cost while maintaining q = 40? (3 pts)