The following equations describe the prices and marginal costs of producing corn and toys in a country. The numbers in the equations indicate the amounts of labor and land needed to produce a unit of corn and a unit of toys. In the equations, the wage rate and the rental rate are denoted by 'w' and 'r,' respectively.Pcorn = 80w + 40rPtoys = 100w + 30ra. If the price per unit of corn and the price per unit of toys are initially $200, calculate the wage rate and the rental rate. Calculate the labor cost per unit of corn and per unit of toys. What is the rental cost per unit of corn and per unit of toys?b. Suppose post-trade the price of corn increases to $240. The price of toys remains unchanged. What are the new values for 'w' and 'r' after adjustment to the new long-run
situation?c. What is the change in the real wage with respect to each good? What is the change in the real rental rate with respect to each good?d. Relate your conclusions in Part C. to the Stolper-Samuelson theorem.
What will be an ideal response?
a. POSSIBLE RESPONSE: To answer this question we need to solve the equations simultaneously:
200 = 80w + 40r
200 = 100w + 30r
The solution is w = $1.25 and r = $2.50. The labor cost per unit of corn output is (80 × 1.25) = $100, and the labor cost per unit of toys is (100 × 1.25) = $125. The rental cost per unit of corn is (40 × 2.5) = $100, and the rental cost per unit of toys is (30 × 2.5) = $75.
b. POSSIBLE RESPONSE: To answer this question we need now to simultaneously solve the equations after putting in the post-trade price of corn:
240 = 80w + 40r
200 = 100w + 30r
The solution is w = $0.50 and r = $5.
c. POSSIBLE RESPONSE: When the initial price of the two goods is $200, the real wage with respect to corn is (1.25/200) = 0.00625, and with respect to toys is (1.25/200) = 0.00625. As the price of corn rises to $240, the real wage with respect to corn is (0.5/240) = 0.00208 and with respect to toys is (0.5/200) = 0.0025. The purchasing power of labor income decreases in terms of both goods.
When the initial value of the two goods is $200, the real rental rates are (2.5/200) = 0.0125 units of corn and (2.5/200) = 0.0125 units of toys. As the price of corn rises to $240, the real rental rates are (5/240) = 0.0208 units of corn and (5/200) = 0.025 units of toys. The purchasing power of landowners has increased with respect to both goods.
d. POSSIBLE RESPONSE: Our findings are consistent with the Stolper-Samuelson theorem. In the context of this problem, the theorem asserts that, as the price of corn increases, the real return (rent) to the factor used intensively in the production of corn (land) increases, and the real return (wage) to the factor used intensively in the production of toys (labor) falls.
You might also like to view...
Use a graph to show the effects of an expansionary monetary policy moving an economy out of recession and to potential real GDP. Explain what happens to aggregate demand, real GDP, and the price level
What will be an ideal response?
If aggregate demand and nominal GDP increase while the price level is constant, we would conclude that
A) the economy is already at full employment. B) the aggregate supply curve is upward sloping. C) the aggregate supply curve is horizontal. D) the aggregate demand curve is vertical.
Compare and contrast the U.S. economic record prior to 1940 and after 1950 . How do the two time periods differ? What best explains the differences according to a macroeconomist?
Over the past several decades, the difference between the labor-force participation rates of men and women in the U.S. has gradually increased
a. True b. False Indicate whether the statement is true or false