Question

Assume that the demand for commodity is represented by the equation P=50-Qd and supply by the equation P=25+Qs, where Qd and Qs are quantity demanded and quantity supplied, respectively and P is price. a. Compute and show on your graph the DWL if the government subsidizes the consumers of the good ( subsidy=$2/unit) b. Explain the gains from this trade.

Answer 1

We need to first draw the demand and supply curves of the market.

Demand function is P=50-Q_d

When P=$0, Q_d=50 and when Q_d=0, P=$50

Then, plotting price on the y-axis and quantity on the x-axis, the intercepts are 50 each.

Supply function is P=25+Q_s

When P = 0, Q_s = -25 , when Q_s= 0, P = $25 and when Q_s = 50, P = $75

Thus, the y-axis intercept and x-axis intercept for the supply function are 25 and -25 respectively.

Now, for equilibrium,

Demand = Supply

Then, 50-Q=25+Q

or, 2Q=25

or, Q=12.5

and P = 25+12.5 = $37.5

If government provides a subsidy of $2 per unit, then consumers have to pay $36.5 per unit whereas, producers will get $38.5 per unit. The new supply curve becomes P=25+Q_s-2 = 23+Q_s. We have shown the diagram in a rough manner.

Then, for equilibrium, Demand=Supply

or, 50-Q=23+Q

or, 2Q=27

or, Q=13.5

Then, price for consumer = 50-13.5 = $36.5(matches what we have considered above)  

Now, DWL = 1/2*(38.5-36.5)*(13.5-12.5) = $1

2. Here, producers gain = Area (C+D)

Consumer's gain = Area (A+B)

Loss in government's revenue = Dead weight loss