Question

Q.1 Consider the DMP model. Low unemployment is a commonly pursued goal of governments. A subsidy, s, 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. (16 marks) a) What is the firm's surplus, consumer/worker surplus and total surplus with the introduction of a subsidy? (2 marks) b) Using Nash Bargaining what is the real wage solution? (2 marks) c) Determine the equation that determines the supply side of the market V(Q) and the demand side of the market, em(1/3,1), (4 marks) d) Solve for equilibrium and show it graphically. (4 marks) e) What is the impact of the subsidy (s) on labour supply (Q) and labour market tightness (), the real wage (w) and the unemployment rate (u)? (4 marks)

Answer 1

DMP MODEL.    ( the complete theory of DMP model )

Given the current high unemployment rates in most advanced economies, it seems natural to focus my remarks about the DMP model on how the model explains current high unemployment.

The DMP model of unemployment is widely accepted as the most realistic account of unemployment based on a careful and full statement of the underlying economic principles governing labor turnover, job-finding rates, and wage determination. Its building blocks are (1) a stochastic model of labor turnover, where workers separate from jobs, become unemployed, and find new jobs, (2) a model of labor-market tightness, with employers choosing job creation volumes and exerting recruiting effort that controls the job-finding rate, in re- sponse to the payoff to job creation, and (3) a bargaining model of wage determination, which sets the incentive to create jobs because employers capture the difference between workers’ productivity and their wages.

Unemployed workers find jobs at a rate that is highly cyclical. It is vastly harder and more time-consuming to find jobs in today’s labor market with 8.6 percent unemployment than in a market with normal unemployment between 5 and 6 percent. Except in times of rapid change in unemployment, the unemployment rate is the ratio of the separation rate to the sum of the separation rate and the job-finding rate.

The model of labor-market tightness is a revolutionary element of the DMP framework. Prior to its development, economists were aware that markets could be tight or slack but lacked models that made tightness a coherent concept. The measure of tightness is the ratio of vacancies to unemployment. In a tight market, employers find it hard and time- consuming to recruit new workers, so vacancies are high. The unemployed find it easy and quick to find jobs, so unemployment is low.

Let W be the present value of the wage that a worker will be paid over the course of a job and let P be the present value of the worker’s contribution to future revenue (the marginal revenue product of labor). Then P − W is the value that hiring a new worker adds to the firm at the moment of the hire, excluding the costs expended earlier to recruit the worker. The choice that a firm makes is whether to pay the cost of holding a vacancy open for a day, at cost k. The expected payoff is the job-filling rate times the benefit of a hire: q(θ)(P −W). In equilibrium, the cost and payoff must be the same, given free entry to vacancy creation, a key assumption of the model. The first of the two central equations of the DMP model is the zero-profit condition,

q(θ)(P − W ) = k. (1)

The third and by far most challenging piece of the DMP model is the model of wage determination. In the canonical DMP model, the worker and employer split the surplus of their match according to the Nash bargain. With the present value of the worker’s reservation value denoted as R and the worker’s share as β, the surplus is P − R and the Nash-bargain wage is

W =R+β(P −R)=βP +(1−β)R. (2)

In a setting where an outside option fixes R, the DMP model is really easy to explain and manipulate. Given P and R, the Nash bargain determines the wage W according to equation (2) and then P − W determines the tightness of the labor market (and thus the unemployment rate) according to equation (1). But in a realistic labor-market setting, R is not set outside the market, but rather depends on conditions in the market.

value of R depends on what wage the worker expects to earn in the job that will be found after a period of search, how long it will take to find that job, and what unemployment benefits the worker receives and what value the worker attributes to not having to work while searching. Although the DMP model has a neat answer to that problem, a luncheon talk is not the place to present it.

according to Shimer

Shimer’s finding did nothing to diminish the hold of the DMP model on economists interested in understanding how unemployment arises in a full equilibrium and what makes it change over time. It did cast some doubt on the assumption that the wage bargain follows Nash and some doubt on Shimer’s choices of parameter values. Mainly it stimulated a huge amount of new work in the DMP framework. The central ideas of DMP still dominate thinking about unemployment from a macro perspective. To continue my commentary and reach the topic of today’s high unemployment, I drop the Nash assumption and replace equation (2) with a more general setup,

W =B(P,θ,x). (3)

Here x is some variable not previously considered that influences the job value. The function B describes some bargaining protocol that makes W less responsive to the marginal revenue product P or to tightness θ and may depend on a new variable x that can keep wages high and thus raise unemployment. Here wage stickiness comes into the story. Because P − W controls labor-market tightness through equation (1), any factor that reduces the response of W to P makes unemployment rise more in response to a given decline in P. Further, if wages are less responsive to tightness θ, tightness is less able to cushion against the effects of changes in P or the new variable x.

It’s critically important to stress that making wage determination less sensitive to some variables is not recrudescence to the primitive pre-DMP idea that unemployment is just a gap between labor supply and labor demand resulting from a non-equilibrium wage. The model continues to describe a full economic equilibrium, where no pair of actors can improve their joint position.

Now let me turn to the possible role of new influences on the wage, the x in equation (3). Many new variables come to mind. For example, unemployment benefits raise the value of the worker’s outside option in the wage bargain—a feature of the DMP model from its beginnings. A dramatic increase in benefits could raise unemployment. Recent research pursuing that idea has confirmed the increase, but suggests it is small.

The GST version of the DMP model can explain high unemployment in today’s economy. With lower inflation as a result of the slack conditions that have prevailed since 2007, real wages paid to new hires are elevated. The payoff from hiring new works is correspondingly lower. It takes a higher job-filling rate to justify new hires and satisfy the zero profit condition of equation (1). The job-finding rate is lower and unemployment is higher.

3.0 Product market (IS curve) 2.8 3.5 percentage point shift 2.6 2.4 2.2 Inflation rate 2.0 1.8 October 2009: Inflation 1.5%, Unemployment 10.1% October 2008: Inflation 1.9%, Unemployment 6.6% 1.6 1.4 1.2 Labor market (Phillips curve) 1.0 15 10 Unemployment rate

by some investigation of the realism of this proposition, summarized in Figure 1. In December 2007, the unemployment rate was 5.0 percent and the rate of inflation was 2.4 percent, measured by the average one-year-ahead forecast for the Consumer Price Index in the Survey of Professional Forecasters (other measures of inflation are quite similar). In December 2009, inflation was 0.8 percentage points lower at 1.6 percent and unemployment was 4.9 percentage points higher. The figure shows the Phillips curve implied by the data. It is in reasonable agreement with Phillips curves from the GST and other models.