Question

You are employed by Tesla to run their car factory. The production function for new cars is F ( L , K ) = L ⋅ K. Currently the wage, w, is $12.50 and the rental rate, r is $1.25. Hint: you'll probably need a calculator for some square roots here. Don’t forget to try the graph at the end even if you have problems with the beginning.

a) (6 points) Find the MRTS and price ratio. Elon Musk (the CEO) calls you up and says you need to produce 400,000 cars this year. Write down the quantity constraint that represents this.

b) (8 points) What are the cost-minimizing demands for labor, L*, and capital, K*? What is your minimized cost, C*?

c) (4 points) One of Elon Musk’s other companies goes bankrupt, and his cost of capital (the rental rate, r) goes all the way up to $12.50. Find the new cost-minimizing demands for labor, L*, and capital, K*?

d) (8 points) On a graph in the (L,K) plane, draw and label the isoquant quantity constraint in this problem. Add an isocost line corresponding to the cost minimization with the price of capital from parts a & b, r = $1.25: label it with C* from part b. Add an isocost line corresponding to the cost minimization with the new price of capital from part c, r = $12.50: label it C2. Label L* and K* at both cost-minimizing points. It doesn’t have to be to scale, but the position of C2 is important.

Answer 1