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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.

 

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Related questions

Suppose that there are two goods (X and Y). The price of X is $2 per unitu, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8Y^.2

Consumer A has an income of $100, and Consumer B has an income of $300.

1. Derive the marginal utlities of goods X and Y for consumer A


2. Derive the marginal utilities of goods X and Y for consumer B


3. Set consumer A's MRS equal to the price ratio. Then use the budget constraint to solve for her optimal bundle


4. Set consumer B's MRS equal to the price ratio. Then use the budget contraint to solve for his optimal consumption bundle.


5. Calculate the MRS for each consumer at their optimal consumption bundles.


6. Suppose that there is another conusmer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's MRS at her optimal consumption bundle? Why?


1 an imperfect market, individual firms

A.are always able to set the price of their product.
B.are able to influence the price of their product.
C.have no influence over the price of their product.

D.take the market price as given.

1 Which of the following is NOT characteristic of a market economy?

Significant government intervention
Little or no government intervention
Buyers and sellers motivated by self-interest
Prices determined by demand and supply

2 In a competitive market, the price of the product is

independently set by each competing seller.
set by the market leader and then copied by other sellers.
jointly set after a meeting of all sellers in the market.
set by market supply and demand.

3 Which of the following firms participates in a competitive market?

A new car manufacturer, such as Ford, Honda, Toyota, or GMC
A software producer, such as Microsoft
A corn farmer
A local electric utility company

4 In an imperfect market, individual firms

are always able to set the price of their product.
are able to influence the price of their product.
have no influence over the price of their product.
take the market price as given.

5 Which of the following firms operates as a monopoly?

A car manufacturer
A local water utility
A corn farmer
A fish vendor at a neighborhood market

6 According to the law of demand, what is the relationship between price and quantity demanded?

Direct
No relationship
Inverse

7 Refer to the following graph. The demand curve slopes downward because
Click to view graphic. (Links to an external site.)

prices and quantity demanded move in opposite directions.
prices and quantity demanded move in the same direction.
prices and quantity demanded have no relationship.
prices and quantity demanded remain unchanged.

8 A change in which of the following will cause a change in the quantity demanded of coffee?

Consumer income
The price of green tea, a substitute for coffee
The number of coffee consumers
The price of coffee

9 Suppose that burgers and fries are complements in consumption. If the price of fries increases

overall demand for burgers will increase.
overall demand for burgers will decrease.
quantity demanded for burgers will increase.
quantity demanded for burgers will decrease.

10 Suppose that Coca Cola and Pepsi are substitutes in consumption. If the price of Coca Cola decreases, then

both the equilibrium price and the quantity of Pepsi demanded will decrease.
both the equilibrium price and the quantity of Pepsi demanded will increase.
the equilibrium price of Pepsi will increase and the quantity demanded of Pepsi will decrease.
the equilibrium price of Pepsi will decrease and the quantity demanded of Pepsi will increase.

11 According to the law of supply, what is the relationship between price and quantity supplied?

Direct
No relationship
Inverse
It depends on the change in price

12 Refer to the graph below. The supply curve is _______________ driven by the law of supply.
Click to view graphic. (Links to an external site.)

Downward sloping
Upward sloping
Perfectly vertical
Perfectly horizontal

13 A change in which of the following will cause a change in the quantity supplied of coffee?

The technology or the production process of making coffee
Anticipation of a change in the price of coffee
The wages of coffee bean pickers
The price of coffee

14 Which of the following will cause a rightward shift in the supply curve for tobacco?

A fall in the number of tobacco farmers in the market
An increase in taxes on tobacco
Removal of government subsidies to tobacco farmers
An improvement in the technology used in the production of tobacco

15 Flour is a factor of production of cupcakes. How will an increase in the price of flour affect the market for cupcakes?

Overall supply will increase
Overall supply will decrease
Quantity supplied will increase
Quantity supplied will decrease

16 Refer to the following image. When a market is in equilibrium, which of the following is true?
Click to view graphic. (Links to an external site.)

Quantity supplied exceeds quantity demanded
Quantity supplied is less than quantity demanded
Quantity supplied is equal to quantity demanded
There is no relationship between quantity supplied and quantity demanded

17 Refer to the following figure. At a price of $15, this market is experiencing a(n)
Click to view graphic. (Links to an external site.)

equilibrium.
shortage.
surplus.
none of the above are true.

18 Refer to the following figure. At a price of $5, this market is experiencing
Click to view graphic. (Links to an external site.)

equilibrium.
a shortage.
a surplus.
None of the above are true.

19 Suppose pasta salad is a normal good. If the price of pasta (a major ingredient in pasta salad) increases and income also increases, the

equilibrium quantity and equilibrium price of pasta salad will increase.
equilibrium quantity of pasta salad will decrease and the equilibrium price of pasta salad may either increase or decrease.
equilibrium quantity of pasta salad may either increase or decrease and the equilibrium price of pasta salad will increase.
equilibrium quantity and equilibrium price of pasta salad will both decrease.

20. What must happen to the market price in order for a shortage to be eliminated?

Price must fall.
Price must rise.
Price must stay the same.
Price may rise or fall depending on the size of the shortage.

Assume that an individual consumes three goods, X, Y, and Z. The marginal utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X, Y, and Z are, respectively, $1, $3, and $5. The total income of the consumer is $65, and the marginal utility schedule is as follows:

Units of good

Marginal utility of X (units)

Marginal utility of Y (units)

Marginal utility of Z (units)

1

12

60

70

2

11

55

60

3

10

48

50

4

9

40

40

5

8

32

30

6

7

24

25

7

6

21

18

8

5

18

10

9

4

15

3

10

3

12

1

(a)Given a $65 income, how much of each good should the consumer purchase to maximize utility?

(b)Suppose income falls to $43 with the same set of prices; what combination will the consumer choose?

(c)Let income fall to $38; let the price of X rise to $5 while the prices of Y and Z remain at $3 and $5. How does the consumer allocate income now? What would you say if the consumer maintained that X is not purchased because he or she could no longer afford it?

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