ECO204Y5 Lecture Notes - Lecture 16: Isocost, Isoquant, Tangent
Should firms rent or purchase K?
- Rent → annual fee
- Purchase → responsible for depreciation cost and opportunity cost
- If markets for K are competitive, the cost to rent is exactly equal to the cost of ownership
- Suppose rental rate (revenues) < user rate of K (cost of running a K-rental business)
o all firms choose to rent, but for the rental business firm owner: cost > revenues --->
negative profits
▪ they must ↑ rental rate of K to cover depreciation and opportunity cost
- Alternatively, rental rates > user cost of K
o All firs will ow, iur their ow depreiatio ad opportuity ost eause it’s
cheaper than renting
o Rental companies must ↓ rental rate until it equals the user cost of K
- For simplicity, assume all firms rent: treat r as the retal rate of K = user ost of Kost of K
o Measured in $/year for each unity of K
Isocost Line (LR analysis) {graph in notebook}
- Illustrates the possible combinations of L and K that can be purchased for a specific $TC given
w,r
- Illustrated as downward sloping: trade-off between L and K
- Isocost lines drawn farther away imply greater $TC, can purchase more L, K
- Graphing: TC = wL + rK → rearranged: K =
-
o
---> vertical axis intercept
o
---> slope of isocost line
- 2 objective with cost minimization
o {in notebook} Case 1: find cost minimizing combinations of L,K that produces a fixed-
level of output, q
▪ Focus on one isoquant (q = fixed level of output)
▪ Tangency between isoquant and isocost lines
• Equal slopes
o
=
▪ At A:
>
>
because using the few units of L, and
too many K
▪ As you ↓KA --> ↑MPK
↓ LA --> ↓MPL ; ore isoost towards poit C
▪ Note: LA < L* ; KA > K*
▪ At B:
<
should reduce usage of L, and increase use of K to get to
point C
o {handout} Case 2: find how costs vary for different levels of output → illustrate LRTC
▪ Determine cost-minimizing combinations of L, K for various levels of output: q1 =
100, q2 = 200, q3 = 300
2016/11/07 → Lecture #16
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Purchase responsible for depreciation cost and opportunity cost. If markets for k are competitive, the cost to rent is exactly equal to the cost of ownership. For simplicity, assume all firms rent: treat (cid:862)r(cid:863) as the re(cid:374)tal rate of k = (cid:894)user (cid:272)ost of k(cid:895)(cid:894)(cid:272)ost of k(cid:895: measured in $/year for each unity of k. Illustrates the possible combinations of l and k that can be purchased for a specific given w,r. Illustrated as downward sloping: trade-off between l and k. Isocost lines drawn farther away imply greater , can purchase more l, k. Graphing: tc = wl + rk rearranged: k = : ---> vertical axis intercept, ---> slope of isocost line. {in notebook} case 1: find cost minimizing combinations of l,k that produces a fixed- level of output, q: focus on one isoquant (q = fixed level of output, tangency between isoquant and isocost lines. (cid:3014)(cid:3013) > (cid:3014)(cid:3012) because using the few units of l, and.
