Question 1 2 pts Production in the long run Trump-pettes ltd\" manufactures tram

Question

Question 1 2 pts Production in the long run Trump-pettes ltd" manufactures trampolines with a production function T 2KL. where T is number of trampolines per hour, K is capital and L is labor. The wage per hour is $10, and the rental cost of capital per hour is $0.50 Suppose that Trump-pettes ltd manufactures 160 trampolines per hour. Find the optimal amount of labor and capital; then compute the long-run cost of production. Please use full integers only. Labor Capital = Cost- Hint: find the MRTS, then write down the two conditions for the optimal input choice and solve the two equations for L and K. Plug the two values of L and K into the cost function. Alternatively: set up the Lagrange function and take derivatives.

Explanation / Answer

MRTS=MpL/MPK=2K/2L=K/L

For cost minimisation MRTS=W/R=10/0.5=20

Thus K/L=20 which implies K=20L

Q=2KL=40L2

When Q=160 L=2 and K=40

Total cost=WL+rK=10(2)+40(0.50)=20+20=40

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