4. Jack and Theresa have utility functions m(D,n) = 100D1 +n respectively, where

Question

4. Jack and Theresa have utility functions m(D,n) = 100D1 +n respectively, where yi is individual i's money spent on other goods and D is the number of digital TV channels, TV is a public good for Jack and Theresa.) The price per channel is PD = 5, Individual i has money m 6, 000. Finally, let g denote individual i's contribution to the public good (i) What is the Pareto efficient level of D? (ii) What is the Nash equilibrium level of D when Jack and Theresa make contributions inde pendently? ii) What is the equilibrium level of D when Theresa commits to a strategy of matching Jack's contribution? Explain the relationship between this answer and the answers to (i) and (i

Explanation / Answer

U1=100D^1/2+Y1; U2=100D^1/2+Y2

Pareto optimaility condition for two goods 1 and 2 is MRS1=MRS2=P1/P2( MRS- marginal rate of substitution and P is price)

MRS=ratio of marginal utilities of two goods.

MUd=dU1/dD=50/D^1/2

MUd/MUy1=Pd/Py1

Pd=5 (given) for 1 channel so from here we get

(50/D^1/2=5 so we get D=100

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