Question

Capital (machines per hour) Q= 50,000 Labor (workers per hour) 10,000 5. Refer to the figure above. A firm has a budget of $200,000 to spend on labor and capital. It is currently producing 50,000 units of output using input bundle "A". The price of capital is $50 per machine hour. The slope of the isocost line (in absolute value) is and at point A the marginal product per dollar spent on labor is the marginal product per dollar spent on capital. a. 2/5; greater than w nidoay iq ( tol b. 2/5; less than 03 mbbudo s 5/2; greater than c. d. 5/2; less than

Please make sure you show ALL of your math, and please make sure your handwriting is clear.

Answer 1

The cost function can be written as: C= wL+rK. Here w= wage rate and r= capital rent.

We are given rent(r) as $50 and cost budget is $200000 now we can plug these values in the above equation and rewrite as:

wL + 50K = 200000

Now we will plug one more point in this equation to get the value of wage (w) here. The point is when capital (k)=0 we can observe from the graph that labour is 10,000. Thus let's plug this value in the above equation to get the value of wage rate.

w(10000) + 50(0)=200000

We get: w = $20

Now we can solve for the slope here: slope from the above equation can be given as: w/r

Thus slope will be: w/r= 20/50= 2/5

Now the marginal product of labour is: increment in the output due to 1 unit change in the labor.

Similarly marginal product of capital is the increment in output due one unit change in capital.

Here at pinot A we can see that the change in output is higher when we change the labor by one unit at point A. Thus MPL is higher than MPK at point A.

Final answer is: slope=2/5 and MPL> MPK

Option A is correct here.