Question

PLEASE ATTACH EXCEL FILE!

A Korean electronic chip manufacturer has a production function given q = L^0.5K^0.5

a. Use Excel to determine the amount of capital, K needed to produce 10 units of output for each value of labor, L starting L=2, and going to L=20 in increments of 1. Plot this isoquant.

(Hint: This formula for the isoquant is 10 =L^0.5K^0.5. Squaring both sides of this equation, we obtain 100=LK. Dividing both sides of the equation by L, we learn that K=100/L.)

b. Use Excel to determine the cost of each of these combinations of labor and capital if the wage rate, w, and the cost of capital, r, are each $30 per unit. Which combination of inputs minimizes the cost of producing 10 units of output?

c. The slope of the isoquant is -100/L². Calculate the slope of the isoquant for each combination of inputs. The slope of the isocost line is –w/r = –30/ 30= –1. Verify that the cost minimizing input combination occurs where the slope of the isoquant equals the slope of the isocost line. Draw the isoquant and the isocost line and show that they are tangent at the cost-minimizing combination of inputs.

Answer 1

We are neither permitted according to the guidelines, nor have any option, to attach any excel file. Right now what can be done is to tell you the methods to do what is required.

The production function is . The output is 10, and hence, the K required can be founded as or or . The formula is given as below.

Pressing enter will give us the first value. Then, copying the cell, and then select-by-drag the rest of the cells, and then by ctrl+v, we will have rest of the values. The excel sheet is given below.

The isoquant can be plotted as below.

(b) For if , The cost of each of these combination can be found as or . Putting it in the sheet, we have the following formula.

The rest of the remaining values can be found by the same copy the first formula cell>selct rest of the cells>paste. The sheet is as below.

The cost is seen to be decreasing and then increasing, and reaches a minimum at C10, ie at K=L=10.

(c) For, , the slope is or or , which is the slope of the isoquant, or MRTS (marginal rate of technical substitution) in particular. The formula can be depicted in the sheet as below.

The rest of the cells can be found with the same copy>select>paste method. The sheet is as below.

As can be seen, the slope of the isoquant is indeed equal to the slope of the isocost, which is equal to -1.

The particular socost line which is tangent to the isoquant at the optimum output have , and hence the equation of the isocost goes as or or . The equation can be used to create the required data of the K, as below.

The rest of the values will be filled using same method of copy>select>paste. The sheet will be as below.

The isocost and isoquant are drawn as the sheet below.