Shopping Externalities and Self Fulfilling Unemployment Fluctuations*

An increase in unemployment of 1 percentage point leads to an increase in the probabilityof meeting a buyer who is unemployed rather than employed of (1 + u )=(1 + e ) = 1:25percentage points.The di¤erence between the probability that an unemployed buyer iswilling to purchase at the reservation price r, 1that an employed buyer is willing to purchase at r, 1The value of a sale to an unemployed buyer is y u (r2(1+ u ) 1 (1+ e ) 1 u , and the probability2(1+ e ) 2 e , is 38 percentage points.calibration, the market power e¤ect of unemployment is roughly 0:44 y u .c)=r = 0:93 y u . Thus, given ourThe demand e¤ect of unemployment isDE =1 + u 21e (r c) (w y1 + e (1 + e ) 2 u ) : (32)rAgain, an increase in unemployment of one percentage point leads to an increase in theprobability of meeting a buyer who is unemployed rather than employed of 1.25 percentagepoints. The probability that an employed buyer is willing to purchase at the price r is 0.96.The di¤erence between the value of a sale to an unemployed and an employed buyer is givenby the di¤erence in their expenditures w y u = 0:15 y u times a(r c)=r = 0:93. Thus,given our calibration, the demand e¤ect of unemployment is approximately 0:17 y u .The captivity e¤ect of unemployment is the …rst term in the third line of (30) and it isnegliglible because e 0. Finally, the multiplier e¤ect is2ME = 1e (r c)S 0 (0): (33)(1 + e ) 2 rAn increase in unemployment of one percentage point leads to an increase in the …rm’sgains from trade of S 0 (0). A fraction of the additional gains from trade is paid out toemployed workers as wages and, hence, increases the value of a sale to an employed workerby S 0 (0)(rc)=r = 0:70 S 0 (0). Thus, the multiplier e¤ect is given by 0:70 S 0 (0) timesthe probability that the …rm sells to an employed worker, 0.96. That is, the multiplier e¤ectis approximately equal to 0:66 S 0 (0).Adding up the market power, demand, captivityand multiplier e¤ects, we conclude that the e¤ect of a one percentage point increase inunemployment on the …rm’s gains from trade in the BJ market is approximately equal toS 0 (0) 0:44 y u + 0:17 y u + 0:66 S 0 (0) =) S 0 (0) 1:8 y u . (34)y eNow, recall that the steady-state value of the …rm is given by J = (+) 1 (1)(S(0)+y u ).. Hence, a one percentage point increase in unemployment leads to a percentage38