Please solve

1. Economists have used the static two-good model to explain some voluntary social distanc- ing observed in data as a rational response to an increase in perceived risk of consuming service-oriented products (cg. dining at a restaurant) during the pandemic. Consider a household in the static two-good model with preferences over two goods1 c1 and c2, represented by the CES utility function: where p 2: 1 is the elasticity of substitution between c1 and egg. The household receives an exogenous ow of income, Y. The rst good, c1, priced at P1 is taken to represent home-produced meals. The second good, c2, priced at Pg, is taken to represent dining at a restaurant. Consuming c2 comes with a perceived transition cost, 1' 2: i}. so that the transaction cost inclusive price is (1 + TJP2. (a) Write down the budget constraint for the household. {b} Express the consumer's optimality condition in terms of the CES utility function. {c} Using your answer from part [b], perform comparative static analysis to show how the cgfc1 ratio is affected following an increase in the transaction cost, and explain in words how the magnitude of this eect depends size of the substitution elasticity. {d} Solve for the household's consumption demand functions for eg- and (22*. {a} Using your answers from part [d], perform comparative static analysis to mathemat- ically show how an increase in the transaction cost 1' causes the optimal values of cu: and Gail to change