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Aggregating preferences for private and public goods a. Suppose Johns demand for tacos is P=6-Q and...

Aggregating preferences for private and public goods

a. Suppose Johns demand for tacos is P=6-Q and Annas demand is P=6-2Q. Write down an equation for the social marginal benefit as a function of Q [i.e. SMB=P=f(Q)] of taco consumption. If the marginal cost of producing each taco constant at $2 per taco, what is the socially optimal number of tacos produced and consumed?

b. Now, suppose Johns demand for fighter jets is P=$10,000,000-(2,000,000*Q) and Annas is P=$5,000,000-(1,000,000*Q). Derive the social marginal benefit (again, P as a function of Q) for the consumption of military fighter jets, which are public goods. If the marginal cost of producing each jet is constant at $3,000,000 per jet, what is the socially optimal number of fighter jets?

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Answer #1

A) Johns demand P=6-Q Or Q=6-P

Anna's demand P=6-2Q Or Q=3-0.5P

thus market demand is the horizontal summation of individual demand curves

Q=Qj + Qa= 9-1.5P   

Marginal cost=$2 Thus at equilibrium P=MC for social optimal

9-1.5(2)=Q=6

Thus P=2 and total quantity=6 Qj=4 and Qa=2

b) For public good demand curve, vertical summation is used in order to get market demand curve

P=P1+P2=15000000-3000000Q

again for social optimal P=Mc=3000000

Q=12000000/3000000=4

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