The Power Rule of Derivatives: Given a functiony-ax3, where a and b are constant

Question

The Power Rule of Derivatives: Given a functiony-ax3, where a and b are constants, its derivative with respect to i:baz1 1. Following the assumptions made in the specific factors model, as- sume the production functions for cloth and food are given by: 1/2r1/2 The total amount of capital available is 400 and the total amount of land is 10,000 a. Find the marginal product of labor employed in the cloth sector and argue that it is decreasing in the amount of labor employed (Hint MPLc is the first order derivative of Qc with respect to Lc.). b. What is the opportunity cost of cloth in terms of food? Does it increase or decrease when employment shifts from cloth to food produc- tion? c. Show graphically that a decrease in the relative world price of cloth leads to a shift away from cloth into food production? d. Show graphically the response of output to a decrease in the relative world price of cloth e. Show graphically that an increase in capital stock (i.e. capital stock in Home increases from 400 to 900) leads to a shift of labor away from food into cloth productio

Explanation / Answer

supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded (at the current price) will equal the quantity supplied (at the current price), resulting in an economic equilibrium for price and quantity transacted.

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