In this exercise your goal is to redo the inter-temporal discrimination model from the class with discounting. As in class, perfectly durable good is sold in two periods to consumers who value it a v per period, where v ~ U(0,1) and marginal cost of production is zero. After the second period the good becomes obsolete and consumers do not value it anymore. Unlike the model in the class, assume that consumers discount the second period at a discount factor dc whereas the firm uses a discount factor Of, where dc, Of [0, 1]. The model from the class is a special case of this model where de = 0; = 1. = (a) Derive optimal prices assuming that consumers are myopic and do not discount the future (de = 1), whereas the firm uses a discount factor dg. Comment on how the solution changes compared to the model without discounting (b) Derive optimal prices when consumers are forward-looking and discount the future payoffs at a rate dc, but the firm does not use discounting (Of - 1). Comment on how pi and p; depend on dc. Explain what happens for dc = 0 and dc = 1. (c) Redo (b) but now assume that it is the firm that discounts future payoffs and not the consumers (dc = 1). Compare the prices you obtain to those from (a) and comment on the differences. = = = In this exercise your goal is to redo the inter-temporal discrimination model from the class with discounting. As in class, perfectly durable good is sold in two periods to consumers who value it a v per period, where v ~ U(0,1) and marginal cost of production is zero. After the second period the good becomes obsolete and consumers do not value it anymore. Unlike the model in the class, assume that consumers discount the second period at a discount factor dc whereas the firm uses a discount factor Of, where dc, Of [0, 1]. The model from the class is a special case of this model where de = 0; = 1. = (a) Derive optimal prices assuming that consumers are myopic and do not discount the future (de = 1), whereas the firm uses a discount factor dg. Comment on how the solution changes compared to the model without discounting (b) Derive optimal prices when consumers are forward-looking and discount the future payoffs at a rate dc, but the firm does not use discounting (Of - 1). Comment on how pi and p; depend on dc. Explain what happens for dc = 0 and dc = 1. (c) Redo (b) but now assume that it is the firm that discounts future payoffs and not the consumers (dc = 1). Compare the prices you obtain to those from (a) and comment on the differences. = = =