# Stock of Capital

Question 1 (6 points)

Give an example of each of the following. You can answer this by drawing rough graphs and giving an explanation in one line in each case (3 points).

y is function of x, but x is not a function of y.

y is not a function of x but x is a function of y.

y is a function of x and x is a function of y.

In each of the following cases, determine the real roots (if any) (3 points) (i) 2×2 -4x + 6 =0 (ii) x2 -2x + 1 =0 (iii) 2×2 -5x + 2=0

## Question 2 (9 points)

Consider an economy with two sectors – food and manufacturing. Each sector uses labour to produce its output, and labour is mobile across both sectors, so that in aggregate labour market equilibrium, workers earn the same wage in both sectors. The supply of labour in the economy is exogenously given. In addition, food requires land and manufacturing requires capital. These factors are not mobile at all, and their quantities are exogenously given. This model can be expressed in terms of the following equations.

1. Lf = a – bw + eT0 a > 0, b > 0, e > 0 2. Lm = c – dw + gK0 c > 0, d > 0, g > 0

Lf +Lm = L0

Equation (1) describes the demand for labour in food production (Lf), where w is the wage and T is the supply of land. Similarly, equation (2) depicts the demand for labour in manufacturing production (Lm), with K standing for the supply of capital. Equation (3) is the equilibrium condition for the economy’s labour market: the total demand for labour should equal the exogenously given supply of labour (L0)

Solve for the equilibrium wage using the equilibrium condition. (3 points)

Determine the impact of an increase in the stock of capital by 2 units on the equilibrium wage. (2 points) Then find the impact on the equilibrium wage of an increase in the stock of land by 2 units. (2 points) Would the equilibrium wage increase, decrease, or remain unchanged if the quantity of capital increased by 2 units and, simultaneously, the quantity of land decreased by 2 units. Explain your answer.(2 points)

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