Question

Dominique only consumes two goods – coffee and French pastries. Her utility function is      U (P,C)...

Dominique only consumes two goods – coffee and French pastries. Her utility function is      U (P,C) = P 0.75 C 0.25, with P being the number of French pastries she consumes and C being the number of cups of coffee she consumes each week. She has $ 32 to allocate on pastries and coffee per week. Note that this is an example of a Cobb-Douglas utility function.

  1. The price of the French pastries is $ 4.00 each, while the price of a cup of coffee is $ 2.00 per cup. Solve for Dominique’s optimal consumption bundle. (6)
  2. Suppose that Dominique receives a frequent customer discount and now she has to pay only $ 2.00 for each pastry she purchases, though she gets no discount on coffee. Assuming nothing else changes, what is her new optimal consumption bundle. (6)

Draw the appropriate diagram to demonstrate your results. Carefully explain your graphical representation of the fall in the price of pastries. Assume that both French pastries and coffee are normal goods

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