Lecture 3 - Theory of Firms Flashcards
(25 cards)
What is the production set in the theory of the firm?
The set of all feasible input–output combinations (x₁, x₂; y) that a firm can produce.
What is an isoquant?
A curve showing all combinations of inputs (x₁, x₂) that yield the same output level y.
Describe the shape of an isoquant for fixed proportions (Leontief) technology.
Right-angle (L-shaped) isoquants reflecting perfect complements: y = min{x₁, x₂}.
Describe the shape of an isoquant for perfect substitutes technology.
Straight-line isoquants with slope –1, reflecting y = x₁ + x₂.
What is the general shape of Cobb–Douglas isoquants?
Smooth, convex curves reflecting y = A·x₁ᵃ·x₂ᵇ.
What is the marginal product of an input?
The additional output produced by a one-unit increase in that input, holding other inputs constant: MPᵢ = ∂f/∂xᵢ.
What is the Technical Rate of Substitution (TRS)?
The slope of the isoquant: TRS = dx₂/dx₁ |_{y=const} = –MP₁/MP₂.
What is the firm’s cost minimization problem?
Minimize w₁x₁ + w₂x₂ subject to f(x₁, x₂) = y.
What is an isocost line?
A line representing all input bundles that cost the same total amount C: w₁x₁ + w₂x₂ = C.
What condition identifies the cost-minimizing input combination?
The tangency condition TRS = w₁/w₂ (i.e., –MP₁/MP₂ = –w₁/w₂).
How is the cost function defined?
c(w₁, w₂, y) = w₁·x₁(w,y) + w₂·x₂(w,y), the minimum cost of producing y at input prices w₁, w₂.
What is average cost (AC)?
AC(y) = c(y)/y, the cost per unit of output.
What is marginal cost (MC)?
MC(y) = dc(y)/dy, the additional cost of producing one more unit of output.
How do average cost (AC) and marginal cost (MC) typically relate?
MC intersects AC at AC’s minimum; MC < AC when AC is falling, MC > AC when AC is rising.
Define profit maximization for a firm.
Choose output y to maximize π(y) = p·y – c(y).
What is the first-order condition for profit maximization?
p = MC(y), where price equals marginal cost.
What distinguishes short run and long run decisions?
In the short run some inputs are fixed; in the long run all inputs are variable.
How is the competitive firm’s supply curve determined?
It’s the portion of its marginal cost curve above the minimum average variable cost (AVC).
What defines a monopoly?
A single seller facing the entire market demand curve (downward-sloping).
How do you calculate marginal revenue (MR) for a monopolist?
MR(y) = d[p(y)·y]/dy = p(y) + y·dp/dy, lying below the demand curve.
What is the monopolist’s profit-maximization condition?
MR(y) = MC(y).
What role does elasticity play in monopoly pricing?
p(1 + 1/ε) = MC, where ε is the price elasticity of demand (ε < 0), implying a markup over MC.
Describe first-degree price discrimination.
Charging each consumer their exact willingness to pay (perfect discrimination).
What is second-degree price discrimination?
Offering a menu of quantity–price bundles so consumers self-select based on usage.
