Answer to Question #193807 in Macroeconomics for ahsan

Question #193807

Suppose the following demand and supply function:

Qd = 750 – 25P

Qs = -300 + 20 P


       i.           Find equilibrium price and quantity

     ii.           Find consumer and producer surplus



1
Expert's answer
2021-05-16T17:42:08-0400

i. At equilibrium:

"Q_s=Q_s \\\\\n\n-300 +20P=750 -25P \\\\\n\n20P+25P = 750 +300 \\\\\n\n45P = 1050 \\\\\n\nP_{eq} = \\frac{1050}{45}=23.33 \\\\\n\nQ_{eq} = -300 +20 \\times 23.33 \\\\\n\n= -300 + 466.66 \\\\\n\n= 166.66"

ii.

"Q_d = 750 -25P"

If Q_d = 0, P_d = 30

Consumer surplus "= \\frac{1}{2}(P_d-P_{eq})Q_{eq}"

"= \\frac{1}{2} \\times(30-23.33)166.66 = 555.611 \\\\\n\nQ_s = -300 + 20P"

If "Q_s = 0, P_s=15"

Producer surplus "= \\frac{1}{2}(P_{eq} -P_s)Q_{eq}"

"= \\frac{1}{2}(23.33-15)166.66 = 693.889"


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