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Millicent runs an Etsy shop on which she sells bracelets (y) made from ounces of beads (z1) and inches of silver-plated wire (z2)
Millicent runs an Etsy shop on which she sells bracelets (y) made from ounces of beads (z1) and inches of silver-plated wire (z2).
Millicent's production function is f(z1, z2) = z1^1/4 z2^3/4 .
The price of an ounce of beads is w1 = 16, the price of an inch of wire is w2 = 3, and the price of output is p = 8.
What is the equation for the isocost line that goes through this input combination?
Solve for the equation
What combination of ounces of beads and inches of wire (z1, z2) should she use to produce these 24 bracelets at lowest possible cost?
Expert Solution
Equation of iscocost line:
C=w1∗z1+w2∗z2=>C=16z1+3z2C=w1∗z1+w2∗z2=>C=16z1+3z2
MP1=∂z1/41z3/42∂z1=>MP1=14(z2z1)34MP2=∂z1/41z3/42∂z2=>MP2=34(z1z2)14Equilibriumcondition:MP1MP2=w1w2=>14(z2z1)3434(z1z2)14=163=>z23z1=163=>z2=16z124=z1/41z3/42=>24=z1/41(16z1)3/4=>24=23z1=>z1=3z2=16∗3=48(z1,z2)=(3,48)
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