Q1. A company has an inverse demand function p = 8 - 0.004Q, and a...

Question

Q1. A company has an inverse demand function p = 8 - 0.004Q, and a...

Q1. A company has an inverse demand function p = 8 - 0.004Q, and a total cost function TC = Q +
0.006Q2. (p is in dollars, and Q is in thousands of units).

a.  What is the optimal price p* and quantity Q* to maximize its profit?

b.  Graph the marginal revenue function and marginal cost function in the (Q, p) space. What is the
slope of each curve? Indicate the intercept of each endpoint in the graph. Indicate the optimal Q* and
p* in the graph.

B What is the point elasticity of demand at (Q*, p*)? Rounding to two decimal places.

C  Suppose now the company adopts a more efficient technology and the cost of producing each
the additional unit reduces by 50 cents.
What is the new marginal cost function? What is the new optimal price and quantity, i.e., Q*new and
p*new? (Hint: the marginal cost reduces by 0.5 dollars).

D Graph the new marginal cost function in the same graph of (2). Indicate the direction of any
movement or shift of the marginal cost function in the graph. Indicate Q*new and p*new.

E Given the new technology, what is the point elasticity of demand at (Q*new, p*new)? Compared with
(3), is it more or less elastic? Rounding to two decimal places.

Q2. Consider again the avocado example, where demand and supply functions are
Qd = 160 - 40p
Qs = 50 + 15p Suppose a severe drought hit California, and the state government decided to subsidize farmers 40 cents
for each pound of avocados produced. (Unit: Q is million pounds of avocados, and p is dollars).

a. With government subsidy, write down the functions of demand and supply.

b. What is the new equilibrium price and quantity of avocados? (Rounding to two decimal places)

c. Plot the demand and supply curves in the same graph. Label your horizontal and vertical axis
properly (you can graph in either (Q, p) or (p, Q) space).
Indicate the end points of each curve on each axis.
Indicate the change of direction for any curve when there is a government subsidy (note: the change of
direction depends on whether you graph in (Q, p) or (p, Q) space).

d What is the price that farmers receive, and the price that consumers pay for each pound of

e  What is the percentage of subsidy pass-through to consumers? What is the percentage of the subsidy
that farmers retain?

f How much in total does the state government have to subsidize the farmers?

g Graph the above demand and supply curves in Excel.
Hint: choose different points of price and quantity to identify the new and old demand and supply
curves; you may find it useful to make a price-quantity table first. Also, note that p and Q cannot be less
than 0.

h Suppose the 40 cents subsidy is given to consumers. Repeat questions in (1)-(7). How do the answers change?

Q3.

The demand and supply for wine are given by Q = 20 - P and Q = 3P, respectively. P is the dollar price
of wine per bottle, and Q is the number of bottles (unit: thousand bottles).

a What is the equilibrium price and quantity?

b Suppose now the government imposes a per-unit tax of \$4 on the sellers. Solve for the new
equilibrium price and quantity, the price sellers received, and the price consumers paid.

c Calculate the government tax revenue.
d What fraction of the tax is passed onto consumers? What fraction of the tax is actually paid by
sellers?

e  If the \$4 tax is collected from consumers, repeat questions (2)-(4). How do your answers to 3-4
change?

Q4.
Assume that the demand for a product X is heavily influenced by the price of another product Y (Py),
and the income of consumers (I).
The cross-price elasticity of X with respect to Y is exy = 1.25, and the income elasticity is eI = 2.
a.. Are X and Y complements or substitutes? Why?
b Is X a normal or inferior good?
c Suppose now Py decreases by 5%, and consumer income decreases by 1%. Will the quantity
demanded of X increase or decrease? By what percent?

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