Question

In: Economics

4. The following is Jim’s production function for wheat. I                 1               2  

4. The following is Jim’s production function for wheat.

I                 1               2               3               4               5               6               7               8               9               10

TP             2               3.7           5.2           6.6           7.9           9.15        10.35     11.5        12.6        13.65

a. What is Jim’s demand for loanable wheat as a function of the real interest rate?

b. What is Jim’s demand for loanable funds, as a function of the nominal interest rate, if the price of wheat is $10 today and will be $10 next year?

c. What is Jim’s demand for loanable funds, as a function of the nominal interest rate if the price of wheat is $10 today and will be $11 next year?

I am a bit confused about these ones

Solutions

Expert Solution

For a firm that produces a good, the number of labor units hired serve as input and total product becomes output. The demand for labor is the marginal product of labor function since it represents real wage rate.

a) In this case the demand for loanable wheat will be a function of marginal product of wheat as a function of interest rate. Find the marginal product of wheat as the additions to successive total products. For example, when interest rate is increased from 2 to 3 percent, TP rises from 3.7 to 5.2 showing an increase of 1.50. This increase becomes smaller and smaller as rate of interest is increased. This is shown in the table below

b) Now price of $10 is same today and next year so inflation rate is 0 and nominal interest rate is same as real interest rate. This implies the demand for loanable wheat is same as in part a)

(Interest rate) TP MP(Demand for loanable wheat part a) and b))
1 2 2
2 3.7 1.7
3 5.2 1.5
4 6.6 1.4
5 7.9 1.3
6 9.15 1.25
7 10.35 1.2
8 11.5 1.15
9 12.6 1.1
10 13.65 1.05

c) Now inflation rate is 10%. Hence nominal interest rate is real interest rate + 10%. The demand function is given below

I(Interest rate) MP(Demand for loanable wheat part c)
11 2
12 1.7
13 1.5
14 1.4
15 1.3
16 1.25
17 1.2
18 1.15
19 1.1
20 1.05

Rahul Sunny answered 2 years ago
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