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Please help me formulate a plan to answer the following question. I am having trouble finding the labor and

capital demands ( I am getting L= Q^2/20 and K=Q^2/500, which doesn't seem to be correct)

finding the MRTS = mpl/mpk, right? where am i going wrong here?

A typical t-shirt maker has a weekly production function represented by Q =10(LK)^.25 where

L is the number of hours of labor employed and K is the units of capital used. The hourly wage of labor is w = $25 and a unit of capital costs r = $1. The firm also has weekly fixed costs of $250.

Find the demands for labor and capital of the typical t-shirt manufacturer. Show that the variable cost is VC = .1Q2.

What is the marginal cost curve of the typical t-shirt manufacturer? What is the average cost? What is the optimal scale of the typical t-shirt manufacturer?

Suppose that the weekly demand is given by the demand function Q = 1150 - 50P.

If the market is perfectly competitive then what is the long run market clearing price?

How many t-shirts are traded at this price? Show that there will be 13 firms in the market.

In a diagram illustrate the market supply curve of the 13 firms and the long run market clearing price and quantity.

Suppose that the demand shifts for t-shirts to Q = 1380 - 50P.

If in the short run there remains only 13 manufacturers in the market, then what will be the new (short run) market clearing price and quantity of t-shirts traded in the market? Illustrate your answer in the diagram above.

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