Question

The table below represents the production function for Hawg Wild, a small catering company specializing in barbecued pork. The numbers in the cells represent the number of customers that can be served with various combinations of labor and capital.

		Labor(L)
	0	1	2	3	4	5	6
	1	100	132	155	174	190	205
Capital (K)	2	152	200	235	264	289	310
	3	193	255	300	337	368	396
	4	230	303	357	400	437	470
	5	263	347	408	457	500	538
	6	293	387	455	510	558	600

a.Is this production function a short-run or long-run production function? How can you tell?

b.Suppose that Hawg Wild employs 5 units of capital and 2 workers. How many diners will be served?

c.Suppose that Hawg Wild employs 5 units of capital and 2 workers, but that the owner, Billy Porcine, is considering adding his nephew to the payroll. What will the marginal product of Billy’s nephew be?

d.Notice that when Hawg Wild uses 1 unit of capital, the marginal product of the fifth unit of labor is 16. But when Hawg Wild uses 5 units of capital, the marginal product of the fifth unit of labor is 43. Does this production function violate the law of diminishing marginal product of labor? Why or why not?

e.Suppose that Hawg Wild employs 5 units of capital and 2 workers, but that the owner, Billy Porcine, is considering adding another meat smoker to the kitchen (which will raise the amount of capital input to 6 units). What will the marginal product of the smoker be?

f. Hawg Wild employs 5 units of capital and 2 workers. Billy is considering the choice between hiring another worker or buying another smoker. If smokers cost $8 and workers $12, then at the margin, what is the most cost-effective choice for Billy to make?

Answer 1

ANS A) This is a long run production function. Since all the inputs are variable. In short run there are both fixed and variable inputs. In the long run production function there are only variable inputs.

B) At K=5 and L = 2 the corresponding value in the table is 347.

Therefore, 347 diners will be served.

C) If owner considers adding nephew. L increases to 3.

At K=5 and L = 3, the corresponding value in the table is 408.

Therefore, 408 diners will be served.

Marginal product of nephew = 408-347 = 61

D) No, Law of diminishing marginal product of labour states that there is a fall in the marginal product of labour with a unit increase in labour while keeping all other inputs constant i.e keeping capital constant.

But in this case we are changing K and keeping L constant which is wrong.

E) At 5 =K and 2=L, the corresponding value in the table is 347.

Adding meat smoker leads to One more K

At 6 =K and 2=L, the corresponding value in the table is 387.

Marginal product of capital = 387-347= 40

F) 5K and 2L and smoker cost = $8, worker cost = $12

cost= 5*8+ 2*12= $ 64.

- if one more K

6K and 2L and smoker cost = $8, worker cost = $12

cost= 6*8+ 2*12=$ 72

- if one more L

5K and 3L and somker cost = $8, worker cost = $12

cost= 5*8+ 3*12= $76

Cost effective choice is hire one more Smokers as $76>$72.