Question
Asked Aug 2, 2019
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please help

1 1
Q(L, K)
50KELE, where K is capital and L is labour. The marginal products are
1 1
1
1
к -LE.
KFL, and MPg
MPL
50
50
Draw a graph showing the short run profit maximization with a few isoprofit
lines and the production function.
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1 1 Q(L, K) 50KELE, where K is capital and L is labour. The marginal products are 1 1 1 1 к -LE. KFL, and MPg MPL 50 50 Draw a graph showing the short run profit maximization with a few isoprofit lines and the production function.

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Expert Answer

Step 1

Let assume that the cost of capital is r and cost of labor (wages) is w

To obtain maximization condition for any function, it must be differentiated wrt to a variable and set equal to zero.

In the short-run capital is constant, so profit function will be differentiated wrt to L and set equal to zero. Let capital be fixed at k-bar.

Profit function can be written as shown below.

 

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Profit function can be written as 7 = py-wL - rK pywL-r) 0 where y= Q = 50 K4/21/2 and p = price (constant) dL (p 501/21/2-wL-rk)=0 d (ri p 50R4/2 p 50 /2 L-1/2-w 1-0 0 w=p50/2 L1/2 = p MP, W w=p MP, or MPL

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Step 2

To graphically represent the profit maximization, let’s say that the maximum profit is equal to an arbitrary number pie-bar

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arbitrary number= 7 p y-wL- rk or wrk y== p wL

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Step 3

The graph with isoprofit line wil...

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Equal slopes of w/p yй Isoprofit line Point of tangency Intercept

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