PADP 6950 Homework 5 - A local farmer raises peaches using land

PADP 6950 Fall 2020 Lawler UGA

Homework 5 Due October 26

1. A local farmer raises peaches using land (K) and labor (L), and has an output of

????(????, ????) = ????0.5????0.5 bushels of peaches. a. Find several input combinations that give the farmer 6 bushels of peaches.

Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis.

b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x- axis and output on the y-axis. What is the name of the slope of this curve?

c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?

d. In the long run, the farmer can change both his amount of land and his amount of labor. Suppose he increases the size of his orchard to 16 units of land. Add to the graph you drew in (b) a new curve showing output as a function of labor when land is fixed at 16.

2. Suppose one of your fellow MPA graduate students is campaigning for an open city council seat. Your friend knows that votes are influenced by TV and newspaper ads according to the following production function:

???????????????????? = 300????????0.6????????0.2,

where TV represents the number of TV ads and NP represents the number of newspaper ads. Thus, the marginal product of a newspaper ad is 60????????0.6????????−0.8 and the marginal product of a TV ad is 180????????−0.4????????0.2. A television ad costs $800 and a local newspaper ad costs $200. Your friend is on a tight budget and needs 1,800 votes to win. What is the lowest-cost combination of TV and newspaper ads that will secure their victory (fractional numbers of ads are fine)? How much will that bundle of ads cost in total?

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