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A local public university is designing a scholarship program…

A local public university is designing a scholarship program to boost enrollment.  We will model scholarships as subsidies paid to consumers (i.e., students) for pursuing degrees.  Everything below can be thought of in thousands — i.e., prices are in thousands of dollars and we consider quantities as thousands of students.  But don’t multiply anything by 1000 here!  The math is meant to be simple.  Let the relationship between supply and the price of tuition be given by the equation qS = 3p. The relationship between demand and the price of tuition is given by the equation qD = 40 – p. Let’s create a benchmark by characterizing equilibrium without scholarships.  Here, tuition is p* = $[p] with q* = [q] students enrolling.   Now let’s introduce scholarships.  These act as a subsidy by driving a wedge between the price that students pay for tuition and the amount that the university receives.  In particular, we say that pS = pD + B, where B is the “size” of the scholarship.  Our new equilibrium condition is that 3pS = 40 – pD. Substitute the identity for pS in terms of pD into the equilibrium condition (making sure to distribute the 3 correctly) and solve for equilibrium prices (with B still on the right-hand side).  Next, plug pS* into qS or pD* into qD to obtain the equilibrium number of students enrolled in terms of B.  If the university seeks to enroll 33 (thousand) students, we must have B* = $[b4].  In this case, we have pS* = $[p1] and pD* = $[p2].  If the university instead seeks to enroll 36 (thousand) students, we must have B** = $[b8].  In this case, we have pS** = $[p3] and pD** = $[p4].

How might certain policies increase or decrease total wages…

How might certain policies increase or decrease total wages paid to workes in a local labor market?  Let’s consider the following model of supply and demand.  The relationship between the quantity of workers supplied and the wage is qS = 3w, while the relationship between the quantity of workers demanded and the wage is qD = 100 – 2w. In the market equilibrium, the wage paid is w* = $[w], and [q] workers are hired.  Total wages paid here are $[tw].   Let’s first consider what happens to total wages when a minimum wage of $25 is imposed.  Here, [q25] workers are hired and total wages paid are $[tw25]. When a minimum wage of $30 is imposed, [q30] workers are hired and total wages paid are $[tw30]. Finally, when a minimum wage of $35 is imposed, [q35] workers are hired and total wages paid are $[tw35].   Now let’s model a payroll tax.  Firms must pay the government $5 per worker hired — this does in a labor market exactly what an excise tax does in a regular market for goods.  While workers receive a wage of wS (remember, workers are the suppliers in a labor market), firms must pay more: wD = wS + 5.  Our new equilibrium condition is that 3wS = 100 – 2wD. Substitute the identity for wD in terms of wS into the equilibrium condition (making sure to distribute the -2 correctly) and solve for wS = $[ws].  This means that we have wD = $[wd], according to our equation.  With the payroll tax, [qpt] workers are hired.  If the government receives $5 per worker hired, let’s now imagine that they send all of this revenue back to workers.  Here, we have total wages paid plus government revenue equal to $[twgr].