Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her production function for jewelry is given by Q = B0.4C0.4 Suppose she can buy beads and copper at prices PB and PC, respectively. (a) Calculate Tiva’s marginal rate of technical substitution between B and C. (b) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost function C(Q) in Lagrangian form. (Note: You do not need to solve it or derive first order conditions.
.2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her production
function for jewelry is given by
Q = B0.4C0.4
Suppose she can buy beads and copper at prices PB and PC, respectively.
(a) Calculate Tiva’s
(b) Does this production function have increasing, constant, or decreasing returns to scale?
Explain.
(c) Set up the cost minimization problem you would use to calculate Tiva’s cost function
C(Q) in Lagrangian form. (Note: You do not need to solve it or derive first order
conditions.
Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The cost
of producing new 3D printed jewelry is
C(Q) = 25 + Q2
4
For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry about
restricting your answers to whole numbers.
(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.
(e) Explain why she will shut down when the market
Tiva’s supply function is given by
QS = 2P
when the price is above her breakeven price. She finds herself in a market where the demand
for her jewelry is given by
QD = 30 −P
In the short run, she is the only one in the market making 3D printed jewelry. However, in
the long run, anyone can enter the market by buying a printer and copying her jewelry for
the same cost.
(f) Compute the short-run
(g) Calculate Tiva’s short-run economic profits.
(h) In the long run, will producers want to enter or exit this market? Explain.
(i) Calculate the long-run equilibrium price and quantity in this market.
(j) On a graph, draw the market demand curve, Tiva’s short-run supply curve, and the
long-run market supply curve.
(k) How much jewelry will Tiva produce at the long-run equilibrium price? What will be
her profits in the long run?
Tiva decides to combat this long-run equilibrium by creating a limited run of jewelry embed-
ded with non-fungible tokens (NFTs) that can never be copied. She creates exactly 10 such
pieces, so that supply of these is perfectly inelastic at 10.
(l) If market demand for these limited pieces is the same as for other jewelry, what will the
equilibrium market price be for these pieces?
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