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1)Use the Solow model to evaluate this question
1)Use the Solow model to evaluate this question. You are the chief economic advisor to a small Caribbean country with an aggregate per capita production function of y = 3k%. The savings rate is 6%, and the rate of depreciation is 10%. Population grows at a rate of 4%. There is no technological progress. a. (3) On a graph, show the output, break-even investment, and savings functions for this economy (as a function of capital per worker). Denote steady-state capital per worker k* and steady-state output per workery". Label your graph completely for full credit.
2)You are the chief economic advisor to a small Caribbean country with an aggregate per capita production function of y = 3k%. The savings rate is 6%, and the rate of depreciation is 10%. Population grows at a rate of 4%. There is no technological progress.
b. (2) Write down the equation used to solve for the steady state, and find the numerical values of this economy's steady-state levels of capital per worker and output per worker. (fractions or decimals are fine)
Use the Solow model to evaluate this question. You are the chief economic advisor to a small Caribbean country with an aggregate per capita production function of y = 3k". The savings rate is 6%, and the rate of depreciation is 10%. Population grows at a rate of 4%. There is no technological progress. a. (3) On a graph, show the output, break-even investment, and savings functions for this economy (as a function of capital per worker). Denote steady-state capital per worker k* and steady-state output per worker y". Label your graph completely for full credit. b. (2) Write down the equation used to solve for the steady state, and find the numerical values of this economy's steady-state levels of capital per worker and output per worker. (fractions or decimals are fine) c. (2) If capital per worker equals four units (k-4), explain in words how the economy works its way toward the steady state.
3)A firms demand function is as follows: Qd = 1200 - P/6
1. At what quantity is the firm's total revenue maximized
2. What price will the firm charge when it maximized total revenue
3. What is the firm's maximum total revenue
Expert Solution
1)We have following information.
y=3k1/2 , saving rate (s) = 0.06, depreciation rate (d) =0.10 and population rate (n) =0.04
Let, i will be the investment per worker.
Break even investment is i = (d+n)k
i = (0.10+0.04)k
i= 0.14k
similarly, s=0.18k1/2
using this information, we have k*=(9/7)2 and y*=27/7
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3)The demand function of the firm is given as Qd=1200-P/6 where Qd and P represent the quantity demanded of the concerned product or service and the price of the product or service respectively. Therefore, the inverse demand function of the product or service would be:P=7200-6Qd. The total revenue function of the firm or TR=P*Q=(7200-6Qd)*Q=7200Q-6Q^2 and the marginal revenue function of the film or MR=dTR/dQ=7200-12Q. Now, when the total revenue of any firm is maximized the marginal revenue of the firm is equal to 0 based on the total revenue maximization principle.
Therefore, based on the total revenue-maximization principle, it can be stated in this case:-
MR=0
7200-12Q=0
-12Q=-7200
Q=-7200/-12
Q*=600
Hence, the total revenue maximizing quantity produced by the firm, in this case, is 600 units.
2. Now, plugging the value of Q* into the demand function of the firm, we get:-
P=7200-6Qd
P=7200-6*(600)
P=7200-3600
P*=3600
Thus, at the total revenue maximized level of production, the firm would charge 3600 to sell it's product or service.
3. The total revenue maximizing price and quantity of the firm are 600 units and 3600 respectively. Therefore, the total revenue of the firm, in this case=(3600*600 units)=2.160,000
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