If the production of tea is cheaper and price of coffee has risen, where will be the new equilibrium for tea?

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Microeconomics

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Identify and Explain Factors affecting Demand and Supply

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Paramjeet ChawlaLv8

29 Oct 2020

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Consider the following exchange economy. There are two goods, tea and coffee, and two consumers, 1 and 2. Consumer 1 has utility function:
𝑈1 (𝑡1, 𝑐1) = 14 𝑙𝑛(𝑡1) + 34 𝑙𝑛(𝑐1) where 𝑡1 and 𝑐1 are the amounts of tea and coffee (respectively) that Consumer 1consumes. Similarly, Consumer 2 has a utility function: 𝑈2 (𝑡2, 𝑐2) = 34 𝑙𝑛(𝑡2) + 14 𝑙𝑛(𝑐2) where 𝑡2 and 𝑐2 denote the amounts of tea and coffee (respectively) that Consumer 2 consumes. Consumer 1 is endowed with 12 units of tea and 32 units of coffee. Consumer 2 is endowed with 4 units of tea and 16 units of coffee. Suppose the price of coffee is normalized to 1, and let p denote the price of tea.
(a) Derive the demand functions of the two consumers for tea and coffee.
(b) Derive the competitive equilibrium price of tea in this economy and the equilibrium quantities of tea and coffee consumed by each consumer.

greenreindeer729

Suppose a caffeine-deprived man needs to wake up. Suppose his preferences on a day can be described by U=3*coffee+2*tea. If the price of coffee is $4 and the price of tea is $1. He has $12 to spend on these drinks on a day.
A. Find his utility for the following consumption combinations:
3 coffee, 0 tea.
1 coffee, 3 tea.
2 coffee, 1.5 tea.
0 coffee, 4.5 tea.
0 coffee, 12 tea.
4 coffee, 6 tea.
8 coffee, 0 tea.
B. Show his budget constraint, indifference curves, and optimal consumption choice in a graph. Use the horizontal axis for coffee and vertical axis for tea.
C. How many cups of coffee does he drink? How many cups of tea? What is his utility?