Solow Model and DMP Model Essay

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ECONOMICS

Consider the DMP model. Low unemployment is a commonly pursued goal of governments. A subsidy, s, is given to firms to encourage more hiring is a policy option that can be implemented with the intended goal of increasing employment and reducing the unemployment rate

1. What is the firm’s surplus, consumer/worker surplus and total surplus with the introduction of a subsidy?

In a successful firm-worker match, the firm produces an output level, z. The firm’s surplus is given by the profit generated from a certain level of output. Assuming a unit price of 1 and that no capital is used in the production process; the firm generates a profit of

Profit = z – w; where w is the real wage paid to the worker

An employment subsidy, S, increases profits by the amount of the subsidy such that:

Profit/firm’s surplus = z – w + s

A worker will only accept a job if the offered wage exceeds the amount of unemployment insurance benefit (b) received. As such, the consumer surplus is given by:

Consumer/Worker Surplus = w – b

Total surplus = consumer surplus + firm’s surplus

= z – w + s + (w – b)

= z + s – b

2. What is the real wage solution using Nash bargaining

Suppose that the worker and firms share the total surplus in the proportion ? and (1- ? ) respectively; the proportion of the surplus attributed to the worker and firm is given by:

Worker surplus: w – b = ? (z + s - b)

Firm’s surplus: z – w + s = (1- ?) (z + s - b)

The real wage solution to the Nash bargaining problem then becomes:

Max (w – b) ? (z – w + s) 1- ? s.t S = z + s – b; yielding the wage equation:

w = ? (z + s) + (1 – ?) b

3. Equations that determine the supply side of the market V (Q) and demand side of the market em(1/j, 1)

The supply side equation:

V(Q) = b + em(1, j) (w – b); but (w-b) = ? (z + s – b)

Thus: V (Q) = b + em (1, j) ? (z + s – b)

The Demand-Side Equation:

Profits are given by: z – w + s;

Firms will post vacancies until the expected payoff from the same is zero such that the product of the probability of finding a worker and the firm’s surplus is equal to capital investment (k) in posting a vacancy.

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Denoting the probability of finding a worker as em (1/j, 1),…

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…per capita is given by:

c* = k* (1 – s)

c* = 2.44 (1-0.2) = 1.952

2. Suppose that savings increase to s=0.4 in the steady state. Determine capital per worker, output per worker, and consumption per capita in the new steady state

Capital per worker;

Kt(? – 1) =

Kt(-0.67) =

Kt(-0.67) = 0.275 ; Introducing logs;

Log 0.275 = - 0.67 log Kt

0.8368 = log Kt

Kt = 6.868

Income per-capita;

y * = k* x (? /(1- ?) = 6.868 x (0.33 / 0.67) = 12.97

Consumption per capita;

Consumption per capita is given by:

c* = k* (1 – s)

c* = 6.868 (1-0.4) = 4.121

3. Suppose that the depreciation rate, d, increases, what is the effect of this change on the quantity of capital per worker and output per worker from the steady state in a above

The equation of capital per worker is = Kt(? – 1)

The equation indicates a direct relationship between depreciation (d) and capital per-worker. An increase in (d) will, therefore, cause an increase in capital per worker (k*)

Income per-capita;

The equation for income per-capita is;

y * = k* x (? /(1- ?)

The increase in k* due to the increase in (d) will cause a subsequent….....

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