In the equilibrium search model, real wages w are determined by the wage curve (WC) equation w = (1 - y)b+ y(y + cy0), where y is worker productivity, y represents workers' bargaining power, c is the recruiting cost (relative to y) to a firm with an open vacancy per time period, and 0 = v/u is labour- market tightness, the ratio of vacancies v to unemployment u. The term b = x + z sums the benefits * paid by the welfare state to an unemployed person and the value of leisure z. Firms open new vacancies to the point where the job-creation (JC) condition (y - w)/(r + s) = cy/q holds, where r is the real interest rate, s is the job-separation rate, and q is the rate at which firms fill vacancies. That rate is q = m/v, where m = AM(u, v) denotes successful matches between jobs and workers. The matching function M(u, v) has constant returns to scale, and positive but diminishing partial derivatives with respect to u and v, and it is the efficiency parameter. Suppose the coronavirus pandemic would have led to a wave of job destruction in the absence of gov- emment policies such as the furlough scheme, which provided public funds for firms to retain workers and pay their wages. Consider a furlough scheme that succeeds in keeping the unemployment rate at its initial steady-state value u*. One benefit of the policy is that it avoids the costs and delays in forming matches again between workers and firms after the pandemic. Consider a time when the pandemic ends, and all parameters return to their pre-pandemic values. In the absence of the furlough scheme, the unemployment rate u is now above u*. (d) Explain why the search model predicts that wages w, market tightness 0, and the job-finding rate f = m/u immediately return to their pre-pandemic values w*, 0*, and f*- (e) Explain why ((y - b)u + xu + cyv) - ((y - bju* + xu* + cyv"), where v* = 0'u", is the loss to the economy if u > u* in a period of time. Show the loss is equal to (y - z + cyd*) (u - u") (0) Show that the law of motion for ut implies Un - * = (1 - s - f)(ut - u*)