3. Suppose Boardwalk cafe is the only shop that sells smoothies at the UWI campus. The marginal cost is 5 dollars per ounce of smoothie. There is a 50-50 chance that a customer is a smoothie addict (high type with O 20) or a regular Joe (low type with 0, 15). Each customer type derives utility from smoothie consumption which is of the form v(q) = 2q"5, and pays a total tariff of T to the cafe. (a) Compute the quantities, tariffs, and expected profit for Boardwalk cafe (i.e., assuming that it can observe the customer's type).

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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3. Suppose Boardwalk cafe is the only shop that sells smoothies at the UWI campus. The marginal cost is 5 dollars
per ounce of smoothie. There is a 50-50 chance that a customer is a smoothie addict (high type with On = 20)
%3D
or a regular Joe (low type with 0 15). Each customer type derives utility from smoothie consumption which
is of the form v(q) = 2q05, and pays a total tariff of T to the cafe.
(a) Compute the quantities, tariffs, and expected profit for Boardwalk cafe (i.e., assuming that it can observe
the customer's type).
(b) Show that in the first best solution, it is also the case that the slope of the isoprofit curve is equal to MRS
for each customer type.
Transcribed Image Text:3. Suppose Boardwalk cafe is the only shop that sells smoothies at the UWI campus. The marginal cost is 5 dollars per ounce of smoothie. There is a 50-50 chance that a customer is a smoothie addict (high type with On = 20) %3D or a regular Joe (low type with 0 15). Each customer type derives utility from smoothie consumption which is of the form v(q) = 2q05, and pays a total tariff of T to the cafe. (a) Compute the quantities, tariffs, and expected profit for Boardwalk cafe (i.e., assuming that it can observe the customer's type). (b) Show that in the first best solution, it is also the case that the slope of the isoprofit curve is equal to MRS for each customer type.
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